Path-oriented Random Testing (PRT) aims at generating a uniformly spread out sequence of random test data that execute a single control flow path within a program. The main challenge of PRT lies in its ability to build efficiently such a test suite in order to minimize the number of rejects (test data that execute another control flow path). We address this problem with an original divide-and-conquer approach based on constraint reasoning over finite domains, a well-recognized Constraint Programming technique. Our approach first derives path conditions by using backward symbolic execution and computes a tight over-approximation of their associated subdomain by using constraint propagation and constraint refutation. Second, a uniform random test data generator is extracted from this approximated subdomain. We implemented this approach and got experimental results that show the practical benefits of PRT based on constraint reasoning. On average, we got a two-order magnitude CPU time improvement over standard Random Testing on a set of paths extracted from classical benchmark programs.